A data consists of $n$ observations
${x_1},{x_2},......,{x_n}.$ If $\sum\limits_{i - 1}^n {{{({x_i} + 1)}^2}} = 9n$ and $\sum\limits_{i - 1}^n {{{({x_i} - 1)}^2}} = 5n,$ then the standard deviation of this data is
$5$
$\sqrt 5$
$\sqrt 7$
$2$
If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt 5$ where $k > 0,$ then $k$ is equal to
Determine mean and standard deviation of first n terms of an $A.P.$ whose first term is a and common difference is d.
If the mean deviation about median for the number $3,5,7,2\,k , 12,16,21,24$ arranged in the ascending order, is $6$ then the median is
If the mean of the data : $7, 8, 9, 7, 8, 7, \mathop \lambda \limits^. , 8$ is $8$, then the variance of this data is
Consider the statistics of two sets of observations as follows :
Size | Mean | Variance | |
Observation $I$ | $10$ | $2$ | $2$ |
Observation $II$ | $n$ | $3$ | $1$ |
If the variance of the combined set of these two observations is $\frac{17}{9},$ then the value of $n$ is equal to ..... .